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- A mixture of short answer and multiple-choice questions
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- Question 1 of 10
##### 1. Question

If the gradient of \(\left( {8,a} \right)\) and \(\left( {-1,3} \right)\) is \(2 \), find the value of \(a \).

\(a = \)

CorrectIncorrect - Question 2 of 10
##### 2. Question

The equation of a straight line perpendicular to \(y = – \dfrac{x}{2} + 4\) and passing through \(\left( {3,1} \right)\) is \(y = Ax + B\).

\(A = \) , \(B = \)

CorrectIncorrect - Question 3 of 10
##### 3. Question

Convert \(34.6^\circ \) to radians, correct to 3 significant figures.

radians

CorrectIncorrect##### Hint

\(\pi \text{ radian } = 180^\circ \)

- Question 4 of 10
##### 4. Question

Find \(A \), if the radius of a circle of the centre angle \(24^\circ \) and the arc length 12 cm is \(\dfrac{A}{\pi }\) cm.

\(A = \)

CorrectIncorrect##### Hint

\(l = r\theta \)

- Question 5 of 10
##### 5. Question

Find the acute angle which has the negative cosine of \(127^\circ \).

CorrectIncorrect - Question 6 of 10
##### 6. Question

If \(\tan x = – \dfrac{4}{3}\) and \(\dfrac{\pi }{2} < x < \pi \), \(\sin x = \dfrac{a}{5}\) and \(\cos x = \dfrac{b}{5}\). Find \(a\) and \(b\).

\(a = \) , \(b = \)

CorrectIncorrect##### Hint

\(\tan \theta = \dfrac{{\sin \theta }}{{\cos \theta }}\)

- Question 7 of 10
##### 7. Question

Find all possible angles \(\theta \) with \(0 \le \theta \le 2\pi \), such that \(\sin \theta = – 1\).

CorrectIncorrect##### Hint

\begin{array} {|c|c|c|c|c|} \hline

& 1^{st} \ Quadrant & 2^{nd} \ Quadrant & 3^{rd} \ Quadrant & 4^{th} \ Quadrant \\ \hline

\text{sin} & + & + & – & – \\ \hline

\text{cos} & + & – & – & + \\ \hline

\text{tan} & + & – & + & – \\ \hline

\end{array} - Question 8 of 10
##### 8. Question

In which quadrant is true where \(\sin \theta \) is positive and \(\cos \theta \) is positive.

CorrectIncorrect - Question 9 of 10
##### 9. Question

Find the first two values of \(t\) when \(h = 5\) given \(y = 5 – 2\cos \dfrac{\pi }{4}\left( {t + 1} \right)\).

,

CorrectIncorrect - Question 10 of 10
##### 10. Question

Find \(A\), if \({\cos ^3}\theta + \cos \theta {\sin ^2}\theta = A\cos \theta \).

\(A = \)

CorrectIncorrect##### Hint

\({\sin ^2}\theta + {\cos ^2}\theta = 1\)